Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Dispersion Analysis of Smoothed Particle Hydrodynamics to Study Convergence and Numerical Phenomena at Coarse Resolution. / Stoyanovskaya, Olga; Lisitsa, Vadim; Anoshin, Sergey et al.
Computational Science and Its Applications - ICCSA 2022 - 22nd International Conference, Proceedings. ed. / Osvaldo Gervasi; Beniamino Murgante; Eligius M. Hendrix; David Taniar; Bernady O. Apduhan. Springer Science and Business Media Deutschland GmbH, 2022. p. 184-197 14 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13375 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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TY - GEN
T1 - Dispersion Analysis of Smoothed Particle Hydrodynamics to Study Convergence and Numerical Phenomena at Coarse Resolution
AU - Stoyanovskaya, Olga
AU - Lisitsa, Vadim
AU - Anoshin, Sergey
AU - Markelova, Tamara
N1 - Publisher Copyright: © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - The Smoothed Particle Hydrodynamics (SPH) method is a meshless Lagrangian method widely used in continuum mechanics simulation. Despite its wide application, theoretical issues of SPH approximation, stability, and convergence are among the unsolved problems of computational mathematics. In this paper, we present the application of dispersion analysis to the SPH approximation of one-dimensional gas dynamics equations to study numerical phenomena that appeared in practice. We confirmed that SPH converges only if the number of particles per wavelength increases while smoothing length decreases. At the same time, reduction of the smoothing length when keeping the number of particles in the kernel fixed (typical convergence results for finite differences and finite elements) does not guarantee the convergence of the numerical solution to the analytical one. We indicate the particular regimes with pronounced irreducible numerical dispersion. For coarse resolution, our theoretical findings are confirmed in simulations.
AB - The Smoothed Particle Hydrodynamics (SPH) method is a meshless Lagrangian method widely used in continuum mechanics simulation. Despite its wide application, theoretical issues of SPH approximation, stability, and convergence are among the unsolved problems of computational mathematics. In this paper, we present the application of dispersion analysis to the SPH approximation of one-dimensional gas dynamics equations to study numerical phenomena that appeared in practice. We confirmed that SPH converges only if the number of particles per wavelength increases while smoothing length decreases. At the same time, reduction of the smoothing length when keeping the number of particles in the kernel fixed (typical convergence results for finite differences and finite elements) does not guarantee the convergence of the numerical solution to the analytical one. We indicate the particular regimes with pronounced irreducible numerical dispersion. For coarse resolution, our theoretical findings are confirmed in simulations.
KW - Convergence analysis
KW - Numerical dispersion
KW - Smoothed particles hydrodynamics (SPH)
UR - http://www.scopus.com/inward/record.url?scp=85135029590&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/9b84c221-9f1f-31b7-b0b8-4c694f0037f7/
U2 - 10.1007/978-3-031-10522-7_14
DO - 10.1007/978-3-031-10522-7_14
M3 - Conference contribution
AN - SCOPUS:85135029590
SN - 9783031105210
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 184
EP - 197
BT - Computational Science and Its Applications - ICCSA 2022 - 22nd International Conference, Proceedings
A2 - Gervasi, Osvaldo
A2 - Murgante, Beniamino
A2 - Hendrix, Eligius M.
A2 - Taniar, David
A2 - Apduhan, Bernady O.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 22nd International Conference on Computational Science and Its Applications, ICCSA 2022
Y2 - 4 July 2022 through 7 July 2022
ER -
ID: 36728693